Question

1] Factor Theorm, x⁴ + 2x³ - 2x² + 2x - 3 by (x+3) 2] Find Acceleration if a car starts from rest and moves with 8m/s and takes 4 sec.

Answer 1

$\red{\underline{{ \bf Question \: 1 }}}$

• Use Factor Theorm to show that x⁴ + 2x³ - 2x² + 2x - 3 is exactly divisible by (x + ).

$\red{\underline{{ \bf Solution }}}$

Let p(x) = x⁴ + 2x³ - 2x² + 2x - 3

Let g(x) = x + 3, then

➱ g(x) = 0

➱ x + 3 = 0

➱ x. = -3

By Factor theorm, p(x) must be exactly divisible by g(x) and would hence give the result as 0.

Now,

➥ p(-3) = {(-3)⁴ + 2 × (-3)³ - 2 × (-3)² + 2 × (-3) - 3}

➥ p(-3) = ( 81 - 54 - 18 - 6 -3 )

➥ p(-3) = 0

Thus, Proved that (x⁴ + 2x³ - 2x² + 2x - 3) is exactly divisible by (x + 3)

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$\red{\underline{{ \bf Question \: 2 }}}$

• Find Acceleration if a car starts from rest and moves with 8m/s and takes 4 sec.

$\red{\underline{{ \bf Answer }}}$

$\underline {\underline{{\purple{ \sf Given }}}}$

• Initial Velocity (u) ⇒ 0 m/s
• Final Velocity (v) ⇒ 8 m/s
• Time Taken (t) ⇒ 4 s

$\underline {\underline{{ \purple{\sf To \: Find }}}}$

• Acceleration (a)

$\underline {\underline{{ \green{\sf Calculating \: Acceleration }}}}$

Formula Used :- $\underline{\underline{\boxed{ \pink{\sf v = u + at }}}}$

Substituting Values

⇉ 8 = 0 + a × 4

⇉ 8 = 0 + 4a

⇉ 8 - 0 = 4a

⇉ 8 = 4a

⇉ 4a = 8

⇉ a = 8/4

⇉ a = 2

Therefore, acceleration of the Car is 2 m/s²

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